logical; if TRUE (default)
probabilities are $P(X \le x)$ otherwise, $P(X > x)$.
log, log.p
logical; if TRUE, probabilities p are given as log(p).
Value
dGPD() computes the density, pGPD() the distribution
function, qGPD() the quantile function and rGPD() random
variates of the generalized Pareto distribution.
Similary for dPar(), pPar(), qPar() and
rPar() for the (standard) Pareto distribution.
Details
The distribution function of the generalized Pareto distribution is given by
$$F(x)=\cases{
1-(1+\xi x/\beta)^{-1/\xi},&if $\xi\neq 0$,\cr
1-\exp(-x/\beta),&if $\xi=0$,\cr}$$
where $\beta>0$ and $x\ge0$ if $\xi\ge 0$
and $x\in[0,-\beta/\xi]$ if $\xi<0$.< p="">
The distribution function of the (standard) Pareto distribution is given by
$$F(x)=1-(1+x)^{-\theta},\ x\ge 0,$$
where $\theta>0$.
In contrast to dGPD(), pGPD(), qGPD() and
rGPD(), the functions dPar(), pPar(),
qPar() and rPar() are vectorized in both their main
argument and $\theta$.
References
McNeil, A. J., Frey, R., and Embrechts, P. (2015).
Quantitative Risk Management: Concepts, Techniques, Tools.
Princeton University Press.